Synchronisation and communication with regularly clocked optoelectronic discrete time chaos M. Grapinet, V.S. Udaltsov, L. Larger and J.M. Dudley A report is presented on the first synchronisation results with two optoelectronic nonlinear delayed feedback subsystems generating sequences of regularly clocked picosecond light pulses with chaoti- cally distributed amplitude. Chaos encoding and decoding of pseudo- random binary information is also demonstrated. The proposed principle is a promising way for securing high-rate communications with chaos at the physical level. Introduction: The principle of chaos synchronisation has been known since 1990, when Pecora and Carroll published their pioneering paper [1]. Chaos-synchronisation in a ‘master-slave’ subsystems pair has been widely and successfully applied to high-dimensional chaotic systems [2–4], and the synchronisation property of two chaotic subsystems is of particular interest for secure communications [5, 6]. Demonstrations of fast chaos-synchronisation in optics have been mainly realised using a continuous time approach (i.e. modelled by a differential equation), with fluctuations in both temporal and amplitude characteristics of signals. In contrast, there has been significant interest in an alternative that allows for temporal regularity, consistent with the constraints standard regularly clocked digital optical network communications. In this Letter, we report on the first experimental investigations of both synchronisation and communication using a high repetition rate discrete time and regularly clocked chaos generator at 2.5 Gbit/s. Principle of operation: The emitter – receiver architecture that we use is a modified version of a previous setup, but working in continuous time [6]. The emitter–receiver pair is shown in Fig. 1. Two synchronised mode- locked fibre lasers (Optcom Calmar, l ¼ 1550 nm) generating 10 ps pulses at 2.5 GHz provide the clocked light-sources on the emitter and receiver sides of the architecture, ensuring the discrete time character of the dynamics [7, 8]. Both emitter and receiver also contain tunable fibre delay-lines (DL e,r ), fast preamplified photodiodes (PD e,r ), and RF- drivers (RFD e,r ) that drive integrated electro-optic Mach-Zehnder modu- lators (MZ e,r ). The driven modulators introduce a normalised nonlinear transformation given by the usual transfer function of a two-wave inter- ferometer: F(t ) ¼ sin 2 [ p . u(t )/(2V p,rf ) þ f 0 ], where u(t ) is the MZ input voltage, V p,rf is the usual electro-optic half wave voltage, and f 0 is a DC offset phase which is used to adjust the operating point of the non- linear function [6, 8]. The elements described above are organised in closed loop at the emitter (for chaotic pulse amplitude generation [7]), and in open loop at the receiver. The receiver is driven by the chaotic pulses generated by the emitter, while the nonlinear modulation by MZ r acts on the receiver laser source. The receiver thus replicates the emitter chaotic pulse sequence through the same discrete time delay nonlinear processing chain [6], provided that all amplitude and timing parameters are properly matched between emitter and receiver. At the receiver input, a fibre coupler (FC) splits the received chaotic pulses into two arms, one used for local chaos replication, and the other serving as the reference chaotic sequence for comparison, using a balanced photodiode pair (BPD). The BPD output allows monitoring of the synchronisation error in the absence of an encoded message, or for a direct message recov- ery when a message is mixed with the chaos at the emitter. On the emitter side, message encoding within the chaotic optical pulses is performed via intensity superposition: the emitter pulsed laser is split in two by an FC with one part chaotically modulated via MZ e , while the other is on-off modulated by an additional Mach- Zehnder (MZ m ). This modulator is driven by a pseudorandom binary sequence with the same bit rate as the pulsed laser clock. Intensity addition is achieved through a polarisation combiner (PC), and with properly crossed polarisation (using a l/2 waveplate) between the message and the chaos pulses. (Note that fast polarisation scrambling of these two orthogonally polarised beams should be used before trans- mission, to prevent message/chaos separation on the transmission channel using a simple polariser for example.) Appropriate biasing of MZ m allows adjustment of the relative masking of the message pulses into the chaotic pulses. Note also the necessary use of a delay line DL m , which allows for simultaneous combination of the message with the chaos in PC. A fibre coupler is then used to split into two the message þ chaos pulses, one serving as the feedback for local chaos generation, the other being sent on the transmission channel. 2.5 GHz pulsed laser synchronised 2.5 GHz pulsed laser emitter receiver transmission channel binary data FC binary data MZ m /2 G G MZ e RFD e RFD r DL m DL s MZ r PD e FC DL e FC PC DL r PD r BPD Fig. 1 Communication system with discrete time chaos synchronisation DL: delay line; FC: fibre coupler; PD: photodiodes; RFD: RF drivers; MZ: Mach Zehnder; PC polarisation combiner Synchronisation: When MZ m is off, synchronisation, or replication, of the chaotic amplitude pulse sequence can be observed at the receiver output (BPD). One can disconnect the direct detection branch after the receiver FC or the MZ r output; this allows monitoring of the received reference chaotic pulses or the locally synchronised ones. Fig. 2 shows the superimposed successive pulses for the received chaotic pulses (Fig. 2a, when light is on the positive input of BPD only), and the cor- responding replica generated by the local discrete time nonlinear delay processing (Fig. 2b, when light is on the negative input of BPD only). The two experimental records obtained with a fast digital sampling oscilloscope (CSA8000, 50 GHz electrical input), show good qualitative agreement, and this has been confirmed by further statistical analysis of the probability amplitude distribution of the pulses, as expected from the study of the discrete time chaos dynamics [8]. Synchronisation between the received and the locally replicated pulse sequence is observed when both optical inputs of BPD are connected, and when only very small residual pulse amplitudes can be seen. This situation actually requires careful emitter and receiver matching for both the amplitude parameters (pulse power, optoelectronic and electro-optic gain, bias of the MZ), and the timing parameters (impulse response of the optoelectronic path, absolute and differential delays). 100 mV/div. 100 mV/div. 20 ps/div. a b c 20 ps/div. 20 ps/div. 100 mV/div. Fig. 2 Synchronisation of chaotic amplitude regularly clocked pulses. Superimposed pulse profiles for: emitter chaos (Fig. 2a), receiver inverted replica (Fig. 2b), synchronisation error between the two (Fig. 2c) Binary communication: When MZ m is modulated by a binary message (‘0’ corresponding to zero output optical intensity, ‘1’ to a bias defined pulse amplitude), the pseudorandom (chaotic) character of the nonlinear delay feedback loop is maintained, and the intensity superposition in the polarisation combiner (PC) leads to the masking of the binary amplitude pulses into the chaotic amplitude pulses generated by MZ e . The masking efficiency can be conveniently adjusted through the tuning of the bias of MZ m , and the message driving amplitude, thus varying the relative amplitude of the ‘1s’ of the message compared to the maximum ampli- tude of the chaotic pulses; a ratio of 1:5 was used in our experiments. This is shown in Fig. 3a, where a mistuning of DL m leads to a temporal separation of the message from the chaotic pulses, thus allowing for the simultaneous observation of the message (left pulse trace in Fig. 3a) with a zero level, and a high level), and the chaos (right pulse trace, revealing however some more probable amplitudes, as was already reported in [8]). Fig. 3b shows the conventional detection result for return-to-zero (RZ) transmission. This can be obtained with our setup when only MZ m transmits light to BPD, i.e. when both outputs of MZ e and MZ r are disconnected. Fig. 3c illustrates the output of BPD, when only MZ e is connected, as in Fig. 3a, but now DL m is properly ELECTRONICS LETTERS 5th June 2008 Vol. 44 No. 12